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Bibliographies
HISTORIA
MATHEMATICA 2 (1975),
605-615
BIBLIOGRAPHIES BY GARRETT
BIRKHOFF AND SUE ANN GARWOOD HARVARD UNIVERSITY
GENERAL History and Historiography of Mathematics: 1. Eric T. Bell, The Development of Mathematics. McGraw-Hill, 1940. 2. N. Bourbaki, Elements d'hlistoire des Math&matiques. Hermann, 1960; 2nd ed., 1969. of Mathematics. Wiley, 1968. 3. Carl Boyer, A History 4. Felix Klein, Entwicklung der Mathematik im 19ten Jahrhundert, 2 vols. Springer, 1927; Chelsea Publ. Co. reprint, 1950. Kline, Mathematical Thought from Ancient to Modern 5. Morris Times. Oxford Univ. Press, 1972. and Research Manual of the History 6. Kenneth May, Bibliography of Mathematics. Univ. of Toronto Press, 1973. 7. George Sarton, The Study of the History of Mathematics. Harvard Univ. Press, 1936; Dover reprint, 1957. 8. D. J. Struik, A Concise History of Mathematics, 2 ~01s. Dover, 1948; Dover reprint, 1967. 9. B. L. van der Waerden, Ontwakende Wetenschap. Noordhoff, 1954. English translation by A. Dresden as Science Awakening, Oxford Univ. Press, 1961. Encyclopedias
10. 11. 12. 13. 14. 1s. 16.
and Anthologies
:
Philosophy of Mathematics. P. Benacerraf and H. Putnam (eds.), Prentice-Hall, 1964. N. Bourbaki, Elgments de Mathgmatique. Hermann, 1940-1966. J. d'Alembert, Dictionnaire raisonne des math&matiques, selections from D. Diderot's Encyclopgdie, Paris: Braisson, 1751. Encyklop;idie der Mathematischen Wissenschaften. B. G. Teubner, 1900-1930. C. Gillispie, Dictionary of Scientific Biography. Scribner, 1970-. W. Ostwald and A. von Oettingen, Ostwalds Klassiker der Engelmann, 1889-1915 for the first Exakten Wissenschaften. 195 issues. D. J. Struik, Source Book in Mathematics, 1200-1800. Harvard Univ. Press, 1964.
Articles:
17.
G. D. Birkhoff,
"Fifty
years
of American
mathematics,"
606
G. Birkhoff American vol. II,
18. 19.
Mathematical
& S.A. Society
Garwood
Semicentennial
HM2 Publications,
270-315, Am. Math. Sot., 1938. of mathematics," Am. Math. H. Weyl, "A half-century Monthly 58 (1951), 523-53. R. L. Wilder, "The origin and growth of mathematical cepts, 'I Bull. Am. Math. Sot. 59 (1953), 423-48.
con-
Of course, no list of general references on the history of mathematics should fail to mention journals devoted to the history of science such as Isis, Mathesis, Archive for the History of Exact Science, and Historia Mathematics. It should also mention mathematical journals which publish regularly articles providing historical insights, such as the American Mathematical Monthly, The Mathematics Teacher, and Scripta Mathematics.
A - HISTORIOGRAPHY Al. A2. A3. A4. AS. A6. A7. A8. A9. AlO. All. A12. A13. A14.
E. T. Bell, Men of Mathematics. Simon and Schuster,1937. Marc Bloch, Apologie pour l'histoire. Colin, 1949. English translation: The Historian's Craft by P. Putnam, Knopf, 1953. E. H. Carr, What is History? Macmillan, 1961. G. R. Elton, The Practice of History. Sydney Univ. Press, 1967. J. Grabiner, "Is mathematical truth time-dependent?", Am. Math. Mon. 81 (1974), 354-365. C. C. Gillispie, The Edge of Objectivity. Princeton Univ. Press, 1960. G. H. Hardy, A Mathematician's Apology. Cambridge (England) Univ. Press, 1941. J. H. Hexter, Doing History. Bloomington (Indiana) Univ. Press, 1971. T. Kuhn, The Structure of Scientific Revolutions. International Encyclopedia of Unified Science, vol. II, #2. Univ. of Chicago Press, 1962. Brit. Jour. fox Phil. I. Lakatos, "Proofs and refutations," of SC. 14 (1963-64), l-25, 120-139, 221-243, 296-342. F. le Lionnais, Les grands courants de la pens&e math&matique. English translation: Dover, 1971. Cahiers du sud, 1948. K. 0. May, "Growth and quality of the mathematical literature," Isis 59 (1968), 363-371. R. Merton, "Priorities in scientific discovery: a chapter in the sociology of science," em. Social. Raview 22 (1957), 635-659. H. Meschkowski, Denkweisen grosser Mathematiker. F. Vieweg, 1961. English translation: Ways of Thought of Great Mathematicians by J. Dyer-Bennet, Holden-Day, 1964.
Bibliographies
HM2 A15. A16. A17.
D. H. Struik, "On the sociology of mathematics," Science and Society 6 (1942), 58-70; "Concerning mathematics," ibid. 1 (1936), 81-101. R. L. Wilder, The Foundations of Mathematics, Wiley, 1952; 2nd ed., 1965. , Evolution of Mathematical Concepts. Wiley, 1968. B-
Bl. B2. B3. B4.
B5. B6. B7. B8. B9. BlO. Bll. B12. B13. B14. BlS.
607
HISTORY OF FOUNDATIONS
P. Alexandroff, $ber den allgemein Dimensionsbegriff...," Math. Annalen 98 (1928), 617-636. P. Alexandroff and H. Hopf, Topologie. Springer, 1935. C. B. Boyer, The Concepts of the Calculus. Columbia Univ. Press, 1939; Harpur Publ. Co. reprint, 1949; Dover reprint. L. E. J. Brouwer, "Beweis der InvarianT der Dimensionenzahl," Math. Annalen 70 (1911), 161-65; "Beweis der Invarianz des n-dimensionalen Gebiets," ibid. 71 (1911), 305-313; see also "Zur Invarianz des n-dimensionalen Gebiets," ibid. 72 (1912), 55-6. "uber den nattirlichen Dimensionsbegriff," J. reine ZAath. 142 (1913), 146-152. A. L. Cauchy, Oeuvres complbtes (12 + 15 ~01s.). GauthierVillars, 1882-1974. "Note sur les series convergentes. ..,'I C. R. Acad. r&i. 36 (1853), 454-459. J. W. Dauben, "The trigonometric background to George Cantor's theory of sets," Arch. Hist. Exact Sci. 7 (1971), 181-216. J. Dirichlet, "Sur la convergence des s6ribs trigonom6triques . . . . " J. reine ang. Math. 4 (1829), 157-169; Ges. Werke, vol. 1, 117-132. P. Dugac, "ElQments d'analyse de Karl Weierstrass," Arch. Hist. Exact Sci. 10 (1973), 41-176. L. Euler, Opera Omnia, 4 series. Ore11 Fiissli and Birkhauser, 1911-. I. Grattan-Guinness, "Bertrand Russell as a philosopher and a mathematician," Bull. bond. Math. Sot. 5 (1973), 328-48. and J. R. Ravetz, Joseph Fourier 1768-1830. MIT Press, 1972. , "Cauchy, Bolzano and the 'new analysis' of the early nineteenth century," Arch. Hist. Exact Sci. 6 (1970), 372-400. . ., "The correspondence between George Cantor and Philip Jourdain," Jahresb. der D.M.v. (1971), part 1, 111-130; "The rediscovery of the Cantor Dedekind correspondence," ibid. 76 (1974-75), 104-139.
608 B16.
B17. B18. B19. B20. B21. B22. B23. 824. B25. 826. B27. B28. B29. B30. B31. 832. B33.
B34. B35. 836.
G. Birkhoff
& S.A.
Garwood
HMZ
, "Towards a biography of George Cantor," Annals Sci. 27 (1971), 345-391 and plates XXV-XXVIII; "The Russell Archives: Some new light on Russell'slogicism," ibid. 31 (1974), 387-406; "Wiener on the logics of Russell and Schroeder . . ..I' ibid. 32 (1975), 103-132. K. Blackwell, J. Thomas (eds.), Russell in Review. -'Hakkert, Toronto, 1975. , Dear Russell - Dear Jourdain (In press). G. H. Hardy, "Sir George Stokes and the concept of uniform convergence," Proc. Camb. Phil. Sot. 19 (1918), 148-156. E. H. Heine, "fiber trigonometrische Reihen," J. reine ang. Math. 71 (1870), 353-365; "Die Elemente der Functionenlehre," ibid. 74 (1872), 172-188. W. Hurewicz and H. Wallman, Dimension Theory. Princeton Univ. Press, 1941. P. Jourdain, "The development of....mathematical logic and the principles of mathematics," Quar. J. Math. 43 (1912), 219-314. . , "The origins of Cauchy's conception of the definite integral and of the continuity of a function," Isis 1 (1913), 661-713. J. L. Lagrange, Oeuvres de Lagrange (J. Serret, G. Darboux, eds.), 14 vols. Gauthier-Villars, 1867-1892. H. Lebesgue, "Non-applicabilitg de continus de dimensions diff&-entes," Math. Annalen 70 (1912), 166-8. R.O.S. Lipschitz, "De explicatione per series trigonometricas . . . , " J. reine ang. Math. 63 (1864), 296-308. K. 0. May, "Biographical Sketch of Henri Lebesgue" in H. Lebesgue, Measure and the Integral, Holden-Day, 1966. K. Menger, Dimensionstheorie. Teubner, 1928. G. Mittag-Leffler, f'Weierstrass et Sonja Kowalewsky," Acta. Math. 39 (1923), 133-198. F.N.M. Moigno, Abbe, begons de calcul diffgrentiel et de calcul intggral. 4 vols. Bachelier, 1840-61. G. Peano, Opere scelte, V. Cassina (ed.), 3 vols., 1957-59. H. PoincarG, "La Science et la M&thode," E. Flammarion, 1908. Translated as Science and Method by F. Maitland, Dover, 1952. Bernhard Riemann, "zber die Darstellbarkeit einer Function durch eine trigonometrische Reihe," Abh. Ges. Wiss. Gijttingen 13 (1866-67), math. Kl., 87-132; Ges. Math. Werke, 1892, 227-271. B.A.W. Russell, Principles of Mathematics. Cambridge Univ. Press, 1900; 2nd ed., Allen & Unwin, 1971. C. D. Broad, "Bertrand Russell as a philosopher and mathematician," Bull. Lond. Math. Sot. 5 (1973), 328-48. A. M. Schonflies, "Die Entwicklung der Lehre von den Punktmannigfaltigkeiten [part l] ,'I Jber. D.M.V. 8 (1900), Part 2.
HMZ B37.
038.
B39. B40.
B41.
Bibliographies
609
"Note iiber eine Eigenschaft, welche P. L. Seidel, discontinuirliche Funktionen derstellen," Abh. Akad. Wiss. (Also [15, Munich, math. phys. Kl., 7 (1847-49), 381-393. #116].) G. G. Stokes, "On the critical values of the sums of periodic series," Trans. Camb. Phil. Sot. 8 (1849), 533583; Mathematical and Physical Papers, vol. 1, 236-313. K.T.W. Weierstrass, Mathematische Werke, 7 ~01s. Mayer and Mliller, 1894-1927. The Philosophy of Alfred North Whitehead, Paul A. Schilpp (ed.), Library of Living Philosophers, vol. III. Northwestern Univ., 1941; 2nd ed., Tudor Publ. Co., 1951. A. P. Yushkevich, "J.A. da Cunha et les fondements de l'analyse infinitesimale," Rev. d'Hist. Sci. 26 (1973), l-22. C - FOUNDATIONS
Cl. c2. c3.
c4.
CS. C6. c7. C8.
c9. ClO. Cll. c12. c13. c14. ClS.
Errett Bishop, Foundations in Constructive Analysis. McGraw-Hill, 1967. See also the important review by Gabriel Stolzenberg, Bull. AMS 76 (1970), 301-23. L.E.J. Brouwer, "Intuitionism and formalism," Bull. AM.5 20 (1913), 81-96. (Reprint [lo, pp. 66-771.) , "Zur BegrUndung der intuitionistische Mathematik," Math. Annalen 93 (192S), 244-57; 95 (1925), 453-72; 96 (1926), 451-88. . ., "Historical background, principles and methods of intuitionism, I' South African J. Science 49 (1952), 139-46. Martin Davis (ed.), The Undecidable. Raven Press, 1965. B. S. Dreben, "False lemmas in Herbrand," Bull. AMS 69 (1963), 699-706. A. A. Fraenkel and Y. Bar-Hillel, Foundations of Set Theory. North-Holland, 1958. Gottlob Frege, Die Grundlagen der Arithmetik, Breslau, 1884 (English translation, Blackwell, Oxford, 1950, 1953; reprinted by Harper, New York, 1960). ., GrundgesZtze der Arithmetik, Jena, 1893; partial English translation, Univ. California Press, Berkeley, 1964. K. Gbdel, "What is Cantor's continuum problem," Am. Math. Monthly 54 (1947), 515-25. Jean van Heijenoort, FromFrege to Giidel. Harvard Univ. Press, 1967. H. von Helmholtz, Schriften zur Erkenntnistheorie. Springer, 1921. Leon Henkin, ed., Proceedings of the Tariski Symposium. Proc. Symp. Pure Math. XXV, Math. Sot., 1974. David Hilbert, Gesammelte Werke, 3 vols., Springer. , Grundlagen der Geometrie. Teubner. Successive editions appearedin1899,1903, 1909, 1913,1922,1927, and1930.
610 C16. c:7. C18. c19. c20. c21. c22. c23. C24. C25. C26. C27. C28. c29. c30. c31. C32. c33. c34. c35. C36. c37.
G. Birkhoff
& S.A. Garwood
HMZ
"Grundlagender LogikundderArithmetik," Int.Math.Cong. Heidelberg (1904), 174-85;Englishtranslationin [Cll, 129-381. S. C. Kleene, Introduction to Metamathematics. van Nostrand, 1952. Felix Klein, "Lectures on mathematics," The Evanston Colloquium (1893), Am. Math. Sot., 1911. "On the tertium non datur principle," A. N. Kolmogorov, Mat. Sbornik 32 (1925), 646-67 (translated in [Cll, pp. 414-371.) W. A. Luxemburg, Applications of Model Theory to Algebra, Rinehart and Winston, 1969. Analysis and Probability. Imre Lakatos, ed., "Problems in the philosophy of mathematics," Proc. Int. Coil. Phil. SC., London,1965, vol. 1 North-Holland Publ. Co., 1967. C.. I. Lewis, A Survey of Symbolic Logic. Univ. Of California Press, 1918. Wandlungen der Mathematischen Denkens. H. Meschkowski, Vieweg, 1956; English translation by J. H. Gayl, Evolution of Mathematical Thought, Holden-Day, 1965. Eugene P. Northrop, Riddles in Mathematics: a book of paradoxes. van Nostrand, 1944. 4 vols. Guiseppe Peano, Formulaire de MathGmatiques. Turin, 1895-1903. 2 vols. G. P6lya, Mathematics of Plausible Reasoning. Princeton Univ. Press, 1954. Hilary Putnam, "Mathematics, Matter, and Method," Philosophical Papers, vol. 1. Cambridge Univ. Press, 1975. W.V.O. Quine, Selected Logic Papers. Random House, 1966. North-Holland, Abraham Robinson, Non-Standard Analysis. Amsterdam, 1966. W. Sierpinski, "L'axiome de M. Zermelo et son role dans la thCorie des ensembles et l'analyse," Bull. Acad. Sci. Cracovie, (A) (1918), 97-152. J. Von Neumann, Collected Works, 6 ~01s. Pergamon, 1961. Hermann Weyl, Gesammelte Abhandlungen, 4 vo 1s. Springer, 1968. "bber die neuen Grundlagenkrise der Mathematik," 10 (1921), 39-79. Ma'Zeits. Philosophy
of Mathematics
and Natural
Science.
Princeton Univ. Press, 1949. (See also Isis 13 (192930), 536-7.) A. N. Whitehead and Bertrand Russell, Principia Mathematics. 3 vols. 1st ed., 1910-13; 2nd ed., 1925-27. Cambridge Univ. Press. Ernst Zermelo, "Untersuchungen Uber die Grundlagen der Mengenlehre," Math. Annalen 65 (1908), 107-28. (English translation in [Cll, pp. 199-2151.) Bibliotheque du Congris International de Philosophie, Vol. 3 ('Logique et Histoire des Sciences"). A. Colin, Paris, 1901.
Bibliographies
HM2
611
D - ALGEBRA Dl. D2. D3. D4. DS. D6. D7. D8. D9. DlO. Dll. D12. D13. D14. D15. D16.
R. Ayoub, "An introduction to the analytic theory of Mathematical Surveys #lo. Am. Math. Sot., 1963. numbers," E. T. Bell, "Fifty years of algebra in America, 1888-1938," Am. Math. Semicentennial Publications, vol. II, l-34. Sot., 1938. G. Birkhoff, "The role of modern algebra in computing," SIAM-AMS Proceedings, vol. IV, l-47. Am. Math. Sot., 1971. , "Current trends in algebra," Am. Math. Monthly 80, (1973). 760-782. ;-"The rise of modern algebra to 1950," Graduate Studies Texas Tech. Univ. Lubbock, Texas (to appear 1975). H. Bohr, Collected Mathematical Works. Khbenhavn: Dansk Matematisk Forening, 1952. A. Borel, Introduction aux Groupes Arithm&iques. Hermann, 1969. , Linear Algebraic Groups. Benjamin, 1969. E. Cartan, "La gbom$trie des groupes simples," Annali di Mat. 4 (1926-7), 209-56. Geuvres Compl&tes, 6 ~01s. Gauthier-Villars, 195255.' H. P. Cartan and S. Eilenberg, Honwlogical Algebra. Prince ton Univ. Press, 1956. J.W.S. Cassells, "L. J. Mordell," Hull. London Math. Sot. 6 (1974), 69-97. Claude Chevalley, Classification des Groupes de Lie Alggbriques, 2 vols., 1956-58; Math. Nzv. 21 (1960), #S696. J. Dieudonn6, Foundations of Modern Analysis. Academic Press. , "The historical development of algebraic geometry," Am. Math. Monthly 79 (1972), 827-866. , Introduction
M. Dekker, D17. D18. D19. D20. D21. D22. D23.
to the
Theory
ofFormal
Groups.
1973.
, Cours de G&m&%rie Alggbrigue, vol. 1. Presses Universitaires de France, 1974. P. G. Lejeune Dirichlet, Werke. G. Reimer, 1889-1897. J. Drach, "Sur 1'intiZgration logique des equations diff&'entielles," Proc. Int. Math. Congress, vol. 1 (1913), 438-497. N. Dunford and J. T. Schwartz, Linear Operators, 3 ~01s. Interscience, 1958, 1963, 1971. L. P. Eisenhart, Continuous Groups of Transformations. Princeton Univ. Press, 1933; Dover reprint, 1961. T. Estermann, Introduction to Modern Prime Number Theory. Cambridge Univ. Press, 1952. G. Frobenius, Gesammelte Abhandlungen (J. P. Serre, ed.).
612
D24. D25. D26. D27. D28. D29. D30. D31. D32. D33. D34. D35. D36. D37. D38. D39. D40. D41. D42. D43. D44. D45. D46. D47. D48. D49. DSO. D51.
G. Birkhoff
E S.A. Garwood
HM2
3 vols. Springer, 1968. G. H. Hardy and M. Riesz, The General Theory of Dirichlet's Series. Cambridge Univ. Press, 1915. and W. W. Rogosinski, Fourier Series. 2nd ed. Cambridge Univ. Press, 1950. H. Hasse, Zahlentheorie. Akad.-Verlag, 1949. S. Helgason, Differential Geometry and Symmetric Spaces. Academic Press, 1962. K. Hensel, Theorie der Algebraischen Zahlen. Teubner, 1908. and G. Landsberg, Theorie der Algebraischen Functionen einer Variabeln.... Leipzig, 1902. D. Husemoller, Fibre Bundles. McGraw-Hill, 1966. E. R. Kolchin, Differential Algebra and Algebraic Groups. Academic Press, 1973. E. Landau, "Theorie der Dirichletschen Reihen," Handbuch der Lehre von der Verteilung der Primzahlen, vol. 2, book 6, 2nd ed. Teubner, 1909. Serge Lang, Diophantine Geometry. Interscience, 1962. , Algebraic Numbers. Addison-Wesley, 1964. , Introduction to Diophantine Approximations. AddisonWesley, 1966. Introduction to Transcendental Numbers. Addisonm;, 1966. S. Lie and F. Engel, Theorie der Transformationsgruppen. Teubner, 1883-93; Chelsea, 1970. J. Lipman, Transcendental Numbers. Queen's Univ. Press, 1966. C. C. Mac Duffee, An Introduction to Abstract Algebra. Wiley, 1940. S. Mac Lane, Homology. Springer, 1963. John Milnor, Introduction to Algebraic K-Theory. Princeton Univ. Press, 1971. L. J. Mordell, "On the rational solutions of...[cubic and quartic equations]," Proc. Camb. Phil. Sot. 21 (1922), 179-92. L. Novf, Origins of Modern Algebra, translated by J. Taner. Prague, Academic Press, 1973. E. Picard, Trait6 d'dnalyse, vol. 3. Gauthier-Villars, 1898. I. Schur, Werke. Ges. Math. J. P. Serre, Corps Locaux. Hermann, 1962. , Lie Algebras and Lie Groups. Benjamin, 1965. &pres&ntations
Lindaires
des Groups Finis.
EAn, 1967. C. L. Siegel, "Approximation algebraischen Zahlen," Math. Zeits. 10 (1921), 173-213. N. E. Steenrod, The Topology ofFibre Bundles. Princeton Univ. Press, 1951. E. Steinitz, "Algebraische Theorie der Ktirper," J. reine
Bibliographies
HM2
D52. D53. D54. D55. D56. D57. D58. D59. D60. D61,
ang. r@th. 137 (1910), 167-309. Republished with an appendix by R. Baer and H. Hasse, de Gruyter, 1939; Chelsea, 1951. algebraische Zahlen," J. A. Thue, "uber Anngherungswerte reine ang. Math. 135 (1909), 284-305. R. S. Varga, Matrix Iterative Analysis. Prentice-Hall, 1962. E. Vessiot, "Methodes d'int6gration elGmentaires," Encyclopedic des sci. math. pures et appliqu&es, tome II, vol. 3, fast. 1 (1910). sur les courbes alg8briques," A. Weil, "L'arithmEtique Acta Math. 52 (1929), 281-315. "Sur un ThBorBme de Mordell ,'I Bull. Sci. Math. 54 (193oj, 182-191. , Vari.56 lCdhl6riennes. Hermann, 1958. Springer, 1967. r Basic Number Theory. H. Whitney, Topological Groups. Lecture Notes, Harvard, 1936. J. H. Wilkinson, The Algebraic Eigenvalue Problem. Clarendon Press, 1956. 0. Zariski, Collected Papers (H. Hironaka and D. Mumford, eds.). MIT Press, 1972-. E-
El. E2. E3. E4. ES. E6. E7.
E8. E9.
613
ANALYSIS
S. Banach, Th&oorie des Opkations 2nd ed., Chelsea, 1962. E. F. Beckenbach and R. Bellman, 1971. A Collection
L&&ares.
Warsaw, 1933;
Inequalities.
Springer,
of Modern Mathematical
Classics:
Analysis,
ed. R. Bellman. Dover, 1961. M. Bernkopf, "The development of function spaces...," See also Archive Hist. Exact Sci. 3 (1966-67), l-96. ibid. 4 (1968), 308-58. G. Birkhoff, edited with the assistance of U. Merzbach, A Source Book in Classical Analysis. Harvard Univ. Press, 1973. 0. Bolza, Lectures on the Calculus ofvariations. Chicago Univ. Press, 1904. Stephen G. Brush, "Functional integrals and statistical physics," Rev. Mod. Phys. 33 (1961), 79-92; "A history of random processes, I . . ..." Archive Hist. Exact Sci. 5 "Mach and atomism," Synthese 18 (1968), (1968), l-36; 192-215. J. B. Diaz and John M. Bownds, "Euler-Cauchy polygons and the local existence of solutions to abstract ordinary differential equations," Funkc. Ekv. 15 (1972), 193-207. and F. T. Metcalf, "Complementary inequalities. I,"
614
G. Birkhoff J. Math.
ElO. Ell. E12. E13. E14. E15. E16.
E18. E19. E20. E21. E22.
Appl.
E24. E25. E26. E27. E28. E29. E30. E31.
39-74.
l-36.
0. D. Kellogg, Foundations of Potential Theory. Springer, 1929. theory and its significance...," George W. Mackey, "Ergodic Advances in Math. 12 (1974), 178-268. J. H. Manheim, The Genesis of Point Set Topology. Macmillan, 1964. A. F. Monna, Functional Analysis in Historical Perspective. 1973; see also "The concept Osthoek Publ. Co., Utrecht, of function..., I' Archive Hist. Exact Sci. 9 (1972), 57-84. E. H. Moore, Introduction to a Form of General Analysis. The New Haven Colloquium. Yale Univ. Press, 1910. C. B. Morrey, Multiple Integrals in the Calculus of Variations. Springer, 1966. See also Lecture Notes on the Theory of Elliptical
E23.
9 (1964),
HM2
Garwood
and F. T. Metcalf, "An analytic proof of Young's inequality," Am. Math. Monthly 77 (1970), 603-9. "Sur quelques points du calcul fonctionnel," M. Fr&het, Rendic. Sot. Mat. Palermo 22 (1906), l-74. P. Halmos, "Mathematics as a creative art," American Scientist (1968), 375-389. G. H. Hardy, D. E. Littlewood and G. P6lya, Inequalities. Cambridge Univ. Press, 1934. T. W. Hawkins, Lebesgue's Theory of Integration, its Origins Univ. Wisconsin Press, 1970. and Developments. D. Hilbert, Griindzuge einer allgemeinen theorie der Teubner, 1912; Chelsea linearen Integralgleichungen. reprint, 1953. "Motion of the lunar perigee...," Acta Math. G. W. Hill, 8 (1886),
E17.
Anal.
& S.A.
Partial
Differential
Equations.
Univ. of Chicago, 1960. de l'integrabilite des &quations G. Peano, "DEmonstration differentielles ordinaires," Math. Annalen 37 (1890), (A pioneer paper written in Peano's symbolic 182-228. logic.) 0. Perron, "Ein neuer Existenzbeweis fiir die Integrale der D'gleichung y' = f(x,y)," Math. Annafen 76 (1915), 471-84. H. Poincare, Les M&thodes Nouvelles de la Mdchanique Cgleste, 3 Vols. Gauthier-Villars, 1892-1899. Bernhard Riemann, Gesammelte Mathematische Werke, 2nd ed. Teubner, 1892; Dover, 1953. F. Riesz, "Untersuchungen Uber Systeme integrierbarer Funktionen," Math. Annalen 69 (1910), 449-495. , Les d'lnconnues.
SystZ‘mes
d'Equations
Lingaires
2 une Infinit6
Gauthier-Villars, 1913. "fiber Lineare Funktionalgleichungen," Acta Math. 41119181. 71-98. S. Saks ,'Th&orie de 1'Intkgrale. Warsaw, 1933. J. A. Shohat and J. D. Tamarkin, The Problem of Moments. Am. Math. Sot., 1943.
HM2 E32.
Bibliographies
615
E. M. Stein,
Singular Integrals and Differentiability of Functions. Princeton Univ. Press, 1970. and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces. Princeton Univ. Press, 1971. M. H. Stone, Linear Transformations in Hilbert Space. Properties
E33. E34. E3.5. E36. E37. E38.
Am. Math. Sot., 1932. E. C. Tit&marsh, Eigenfunction Expansions. Clarendon Press, 1946. The Analytical Foundations of Celestial A. Wintner, Mechanics. Princeton Univ. Press, 1941. Z. Zygmund, Trigonometric Series, 2 ~01s. Cambridge Univ. Press, 1968. , "IntQgrales Singulikres." Springer Lecture Notes in Math. #204 (1971).
MATHEMATICA 2 (1975),
605-615
BIBLIOGRAPHIES BY GARRETT
BIRKHOFF AND SUE ANN GARWOOD HARVARD UNIVERSITY
GENERAL History and Historiography of Mathematics: 1. Eric T. Bell, The Development of Mathematics. McGraw-Hill, 1940. 2. N. Bourbaki, Elements d'hlistoire des Math&matiques. Hermann, 1960; 2nd ed., 1969. of Mathematics. Wiley, 1968. 3. Carl Boyer, A History 4. Felix Klein, Entwicklung der Mathematik im 19ten Jahrhundert, 2 vols. Springer, 1927; Chelsea Publ. Co. reprint, 1950. Kline, Mathematical Thought from Ancient to Modern 5. Morris Times. Oxford Univ. Press, 1972. and Research Manual of the History 6. Kenneth May, Bibliography of Mathematics. Univ. of Toronto Press, 1973. 7. George Sarton, The Study of the History of Mathematics. Harvard Univ. Press, 1936; Dover reprint, 1957. 8. D. J. Struik, A Concise History of Mathematics, 2 ~01s. Dover, 1948; Dover reprint, 1967. 9. B. L. van der Waerden, Ontwakende Wetenschap. Noordhoff, 1954. English translation by A. Dresden as Science Awakening, Oxford Univ. Press, 1961. Encyclopedias
10. 11. 12. 13. 14. 1s. 16.
and Anthologies
:
Philosophy of Mathematics. P. Benacerraf and H. Putnam (eds.), Prentice-Hall, 1964. N. Bourbaki, Elgments de Mathgmatique. Hermann, 1940-1966. J. d'Alembert, Dictionnaire raisonne des math&matiques, selections from D. Diderot's Encyclopgdie, Paris: Braisson, 1751. Encyklop;idie der Mathematischen Wissenschaften. B. G. Teubner, 1900-1930. C. Gillispie, Dictionary of Scientific Biography. Scribner, 1970-. W. Ostwald and A. von Oettingen, Ostwalds Klassiker der Engelmann, 1889-1915 for the first Exakten Wissenschaften. 195 issues. D. J. Struik, Source Book in Mathematics, 1200-1800. Harvard Univ. Press, 1964.
Articles:
17.
G. D. Birkhoff,
"Fifty
years
of American
mathematics,"
606
G. Birkhoff American vol. II,
18. 19.
Mathematical
& S.A. Society
Garwood
Semicentennial
HM2 Publications,
270-315, Am. Math. Sot., 1938. of mathematics," Am. Math. H. Weyl, "A half-century Monthly 58 (1951), 523-53. R. L. Wilder, "The origin and growth of mathematical cepts, 'I Bull. Am. Math. Sot. 59 (1953), 423-48.
con-
Of course, no list of general references on the history of mathematics should fail to mention journals devoted to the history of science such as Isis, Mathesis, Archive for the History of Exact Science, and Historia Mathematics. It should also mention mathematical journals which publish regularly articles providing historical insights, such as the American Mathematical Monthly, The Mathematics Teacher, and Scripta Mathematics.
A - HISTORIOGRAPHY Al. A2. A3. A4. AS. A6. A7. A8. A9. AlO. All. A12. A13. A14.
E. T. Bell, Men of Mathematics. Simon and Schuster,1937. Marc Bloch, Apologie pour l'histoire. Colin, 1949. English translation: The Historian's Craft by P. Putnam, Knopf, 1953. E. H. Carr, What is History? Macmillan, 1961. G. R. Elton, The Practice of History. Sydney Univ. Press, 1967. J. Grabiner, "Is mathematical truth time-dependent?", Am. Math. Mon. 81 (1974), 354-365. C. C. Gillispie, The Edge of Objectivity. Princeton Univ. Press, 1960. G. H. Hardy, A Mathematician's Apology. Cambridge (England) Univ. Press, 1941. J. H. Hexter, Doing History. Bloomington (Indiana) Univ. Press, 1971. T. Kuhn, The Structure of Scientific Revolutions. International Encyclopedia of Unified Science, vol. II, #2. Univ. of Chicago Press, 1962. Brit. Jour. fox Phil. I. Lakatos, "Proofs and refutations," of SC. 14 (1963-64), l-25, 120-139, 221-243, 296-342. F. le Lionnais, Les grands courants de la pens&e math&matique. English translation: Dover, 1971. Cahiers du sud, 1948. K. 0. May, "Growth and quality of the mathematical literature," Isis 59 (1968), 363-371. R. Merton, "Priorities in scientific discovery: a chapter in the sociology of science," em. Social. Raview 22 (1957), 635-659. H. Meschkowski, Denkweisen grosser Mathematiker. F. Vieweg, 1961. English translation: Ways of Thought of Great Mathematicians by J. Dyer-Bennet, Holden-Day, 1964.
Bibliographies
HM2 A15. A16. A17.
D. H. Struik, "On the sociology of mathematics," Science and Society 6 (1942), 58-70; "Concerning mathematics," ibid. 1 (1936), 81-101. R. L. Wilder, The Foundations of Mathematics, Wiley, 1952; 2nd ed., 1965. , Evolution of Mathematical Concepts. Wiley, 1968. B-
Bl. B2. B3. B4.
B5. B6. B7. B8. B9. BlO. Bll. B12. B13. B14. BlS.
607
HISTORY OF FOUNDATIONS
P. Alexandroff, $ber den allgemein Dimensionsbegriff...," Math. Annalen 98 (1928), 617-636. P. Alexandroff and H. Hopf, Topologie. Springer, 1935. C. B. Boyer, The Concepts of the Calculus. Columbia Univ. Press, 1939; Harpur Publ. Co. reprint, 1949; Dover reprint. L. E. J. Brouwer, "Beweis der InvarianT der Dimensionenzahl," Math. Annalen 70 (1911), 161-65; "Beweis der Invarianz des n-dimensionalen Gebiets," ibid. 71 (1911), 305-313; see also "Zur Invarianz des n-dimensionalen Gebiets," ibid. 72 (1912), 55-6. "uber den nattirlichen Dimensionsbegriff," J. reine ZAath. 142 (1913), 146-152. A. L. Cauchy, Oeuvres complbtes (12 + 15 ~01s.). GauthierVillars, 1882-1974. "Note sur les series convergentes. ..,'I C. R. Acad. r&i. 36 (1853), 454-459. J. W. Dauben, "The trigonometric background to George Cantor's theory of sets," Arch. Hist. Exact Sci. 7 (1971), 181-216. J. Dirichlet, "Sur la convergence des s6ribs trigonom6triques . . . . " J. reine ang. Math. 4 (1829), 157-169; Ges. Werke, vol. 1, 117-132. P. Dugac, "ElQments d'analyse de Karl Weierstrass," Arch. Hist. Exact Sci. 10 (1973), 41-176. L. Euler, Opera Omnia, 4 series. Ore11 Fiissli and Birkhauser, 1911-. I. Grattan-Guinness, "Bertrand Russell as a philosopher and a mathematician," Bull. bond. Math. Sot. 5 (1973), 328-48. and J. R. Ravetz, Joseph Fourier 1768-1830. MIT Press, 1972. , "Cauchy, Bolzano and the 'new analysis' of the early nineteenth century," Arch. Hist. Exact Sci. 6 (1970), 372-400. . ., "The correspondence between George Cantor and Philip Jourdain," Jahresb. der D.M.v. (1971), part 1, 111-130; "The rediscovery of the Cantor Dedekind correspondence," ibid. 76 (1974-75), 104-139.
608 B16.
B17. B18. B19. B20. B21. B22. B23. 824. B25. 826. B27. B28. B29. B30. B31. 832. B33.
B34. B35. 836.
G. Birkhoff
& S.A.
Garwood
HMZ
, "Towards a biography of George Cantor," Annals Sci. 27 (1971), 345-391 and plates XXV-XXVIII; "The Russell Archives: Some new light on Russell'slogicism," ibid. 31 (1974), 387-406; "Wiener on the logics of Russell and Schroeder . . ..I' ibid. 32 (1975), 103-132. K. Blackwell, J. Thomas (eds.), Russell in Review. -'Hakkert, Toronto, 1975. , Dear Russell - Dear Jourdain (In press). G. H. Hardy, "Sir George Stokes and the concept of uniform convergence," Proc. Camb. Phil. Sot. 19 (1918), 148-156. E. H. Heine, "fiber trigonometrische Reihen," J. reine ang. Math. 71 (1870), 353-365; "Die Elemente der Functionenlehre," ibid. 74 (1872), 172-188. W. Hurewicz and H. Wallman, Dimension Theory. Princeton Univ. Press, 1941. P. Jourdain, "The development of....mathematical logic and the principles of mathematics," Quar. J. Math. 43 (1912), 219-314. . , "The origins of Cauchy's conception of the definite integral and of the continuity of a function," Isis 1 (1913), 661-713. J. L. Lagrange, Oeuvres de Lagrange (J. Serret, G. Darboux, eds.), 14 vols. Gauthier-Villars, 1867-1892. H. Lebesgue, "Non-applicabilitg de continus de dimensions diff&-entes," Math. Annalen 70 (1912), 166-8. R.O.S. Lipschitz, "De explicatione per series trigonometricas . . . , " J. reine ang. Math. 63 (1864), 296-308. K. 0. May, "Biographical Sketch of Henri Lebesgue" in H. Lebesgue, Measure and the Integral, Holden-Day, 1966. K. Menger, Dimensionstheorie. Teubner, 1928. G. Mittag-Leffler, f'Weierstrass et Sonja Kowalewsky," Acta. Math. 39 (1923), 133-198. F.N.M. Moigno, Abbe, begons de calcul diffgrentiel et de calcul intggral. 4 vols. Bachelier, 1840-61. G. Peano, Opere scelte, V. Cassina (ed.), 3 vols., 1957-59. H. PoincarG, "La Science et la M&thode," E. Flammarion, 1908. Translated as Science and Method by F. Maitland, Dover, 1952. Bernhard Riemann, "zber die Darstellbarkeit einer Function durch eine trigonometrische Reihe," Abh. Ges. Wiss. Gijttingen 13 (1866-67), math. Kl., 87-132; Ges. Math. Werke, 1892, 227-271. B.A.W. Russell, Principles of Mathematics. Cambridge Univ. Press, 1900; 2nd ed., Allen & Unwin, 1971. C. D. Broad, "Bertrand Russell as a philosopher and mathematician," Bull. Lond. Math. Sot. 5 (1973), 328-48. A. M. Schonflies, "Die Entwicklung der Lehre von den Punktmannigfaltigkeiten [part l] ,'I Jber. D.M.V. 8 (1900), Part 2.
HMZ B37.
038.
B39. B40.
B41.
Bibliographies
609
"Note iiber eine Eigenschaft, welche P. L. Seidel, discontinuirliche Funktionen derstellen," Abh. Akad. Wiss. (Also [15, Munich, math. phys. Kl., 7 (1847-49), 381-393. #116].) G. G. Stokes, "On the critical values of the sums of periodic series," Trans. Camb. Phil. Sot. 8 (1849), 533583; Mathematical and Physical Papers, vol. 1, 236-313. K.T.W. Weierstrass, Mathematische Werke, 7 ~01s. Mayer and Mliller, 1894-1927. The Philosophy of Alfred North Whitehead, Paul A. Schilpp (ed.), Library of Living Philosophers, vol. III. Northwestern Univ., 1941; 2nd ed., Tudor Publ. Co., 1951. A. P. Yushkevich, "J.A. da Cunha et les fondements de l'analyse infinitesimale," Rev. d'Hist. Sci. 26 (1973), l-22. C - FOUNDATIONS
Cl. c2. c3.
c4.
CS. C6. c7. C8.
c9. ClO. Cll. c12. c13. c14. ClS.
Errett Bishop, Foundations in Constructive Analysis. McGraw-Hill, 1967. See also the important review by Gabriel Stolzenberg, Bull. AMS 76 (1970), 301-23. L.E.J. Brouwer, "Intuitionism and formalism," Bull. AM.5 20 (1913), 81-96. (Reprint [lo, pp. 66-771.) , "Zur BegrUndung der intuitionistische Mathematik," Math. Annalen 93 (192S), 244-57; 95 (1925), 453-72; 96 (1926), 451-88. . ., "Historical background, principles and methods of intuitionism, I' South African J. Science 49 (1952), 139-46. Martin Davis (ed.), The Undecidable. Raven Press, 1965. B. S. Dreben, "False lemmas in Herbrand," Bull. AMS 69 (1963), 699-706. A. A. Fraenkel and Y. Bar-Hillel, Foundations of Set Theory. North-Holland, 1958. Gottlob Frege, Die Grundlagen der Arithmetik, Breslau, 1884 (English translation, Blackwell, Oxford, 1950, 1953; reprinted by Harper, New York, 1960). ., GrundgesZtze der Arithmetik, Jena, 1893; partial English translation, Univ. California Press, Berkeley, 1964. K. Gbdel, "What is Cantor's continuum problem," Am. Math. Monthly 54 (1947), 515-25. Jean van Heijenoort, FromFrege to Giidel. Harvard Univ. Press, 1967. H. von Helmholtz, Schriften zur Erkenntnistheorie. Springer, 1921. Leon Henkin, ed., Proceedings of the Tariski Symposium. Proc. Symp. Pure Math. XXV, Math. Sot., 1974. David Hilbert, Gesammelte Werke, 3 vols., Springer. , Grundlagen der Geometrie. Teubner. Successive editions appearedin1899,1903, 1909, 1913,1922,1927, and1930.
610 C16. c:7. C18. c19. c20. c21. c22. c23. C24. C25. C26. C27. C28. c29. c30. c31. C32. c33. c34. c35. C36. c37.
G. Birkhoff
& S.A. Garwood
HMZ
"Grundlagender LogikundderArithmetik," Int.Math.Cong. Heidelberg (1904), 174-85;Englishtranslationin [Cll, 129-381. S. C. Kleene, Introduction to Metamathematics. van Nostrand, 1952. Felix Klein, "Lectures on mathematics," The Evanston Colloquium (1893), Am. Math. Sot., 1911. "On the tertium non datur principle," A. N. Kolmogorov, Mat. Sbornik 32 (1925), 646-67 (translated in [Cll, pp. 414-371.) W. A. Luxemburg, Applications of Model Theory to Algebra, Rinehart and Winston, 1969. Analysis and Probability. Imre Lakatos, ed., "Problems in the philosophy of mathematics," Proc. Int. Coil. Phil. SC., London,1965, vol. 1 North-Holland Publ. Co., 1967. C.. I. Lewis, A Survey of Symbolic Logic. Univ. Of California Press, 1918. Wandlungen der Mathematischen Denkens. H. Meschkowski, Vieweg, 1956; English translation by J. H. Gayl, Evolution of Mathematical Thought, Holden-Day, 1965. Eugene P. Northrop, Riddles in Mathematics: a book of paradoxes. van Nostrand, 1944. 4 vols. Guiseppe Peano, Formulaire de MathGmatiques. Turin, 1895-1903. 2 vols. G. P6lya, Mathematics of Plausible Reasoning. Princeton Univ. Press, 1954. Hilary Putnam, "Mathematics, Matter, and Method," Philosophical Papers, vol. 1. Cambridge Univ. Press, 1975. W.V.O. Quine, Selected Logic Papers. Random House, 1966. North-Holland, Abraham Robinson, Non-Standard Analysis. Amsterdam, 1966. W. Sierpinski, "L'axiome de M. Zermelo et son role dans la thCorie des ensembles et l'analyse," Bull. Acad. Sci. Cracovie, (A) (1918), 97-152. J. Von Neumann, Collected Works, 6 ~01s. Pergamon, 1961. Hermann Weyl, Gesammelte Abhandlungen, 4 vo 1s. Springer, 1968. "bber die neuen Grundlagenkrise der Mathematik," 10 (1921), 39-79. Ma'Zeits. Philosophy
of Mathematics
and Natural
Science.
Princeton Univ. Press, 1949. (See also Isis 13 (192930), 536-7.) A. N. Whitehead and Bertrand Russell, Principia Mathematics. 3 vols. 1st ed., 1910-13; 2nd ed., 1925-27. Cambridge Univ. Press. Ernst Zermelo, "Untersuchungen Uber die Grundlagen der Mengenlehre," Math. Annalen 65 (1908), 107-28. (English translation in [Cll, pp. 199-2151.) Bibliotheque du Congris International de Philosophie, Vol. 3 ('Logique et Histoire des Sciences"). A. Colin, Paris, 1901.
Bibliographies
HM2
611
D - ALGEBRA Dl. D2. D3. D4. DS. D6. D7. D8. D9. DlO. Dll. D12. D13. D14. D15. D16.
R. Ayoub, "An introduction to the analytic theory of Mathematical Surveys #lo. Am. Math. Sot., 1963. numbers," E. T. Bell, "Fifty years of algebra in America, 1888-1938," Am. Math. Semicentennial Publications, vol. II, l-34. Sot., 1938. G. Birkhoff, "The role of modern algebra in computing," SIAM-AMS Proceedings, vol. IV, l-47. Am. Math. Sot., 1971. , "Current trends in algebra," Am. Math. Monthly 80, (1973). 760-782. ;-"The rise of modern algebra to 1950," Graduate Studies Texas Tech. Univ. Lubbock, Texas (to appear 1975). H. Bohr, Collected Mathematical Works. Khbenhavn: Dansk Matematisk Forening, 1952. A. Borel, Introduction aux Groupes Arithm&iques. Hermann, 1969. , Linear Algebraic Groups. Benjamin, 1969. E. Cartan, "La gbom$trie des groupes simples," Annali di Mat. 4 (1926-7), 209-56. Geuvres Compl&tes, 6 ~01s. Gauthier-Villars, 195255.' H. P. Cartan and S. Eilenberg, Honwlogical Algebra. Prince ton Univ. Press, 1956. J.W.S. Cassells, "L. J. Mordell," Hull. London Math. Sot. 6 (1974), 69-97. Claude Chevalley, Classification des Groupes de Lie Alggbriques, 2 vols., 1956-58; Math. Nzv. 21 (1960), #S696. J. Dieudonn6, Foundations of Modern Analysis. Academic Press. , "The historical development of algebraic geometry," Am. Math. Monthly 79 (1972), 827-866. , Introduction
M. Dekker, D17. D18. D19. D20. D21. D22. D23.
to the
Theory
ofFormal
Groups.
1973.
, Cours de G&m&%rie Alggbrigue, vol. 1. Presses Universitaires de France, 1974. P. G. Lejeune Dirichlet, Werke. G. Reimer, 1889-1897. J. Drach, "Sur 1'intiZgration logique des equations diff&'entielles," Proc. Int. Math. Congress, vol. 1 (1913), 438-497. N. Dunford and J. T. Schwartz, Linear Operators, 3 ~01s. Interscience, 1958, 1963, 1971. L. P. Eisenhart, Continuous Groups of Transformations. Princeton Univ. Press, 1933; Dover reprint, 1961. T. Estermann, Introduction to Modern Prime Number Theory. Cambridge Univ. Press, 1952. G. Frobenius, Gesammelte Abhandlungen (J. P. Serre, ed.).
612
D24. D25. D26. D27. D28. D29. D30. D31. D32. D33. D34. D35. D36. D37. D38. D39. D40. D41. D42. D43. D44. D45. D46. D47. D48. D49. DSO. D51.
G. Birkhoff
E S.A. Garwood
HM2
3 vols. Springer, 1968. G. H. Hardy and M. Riesz, The General Theory of Dirichlet's Series. Cambridge Univ. Press, 1915. and W. W. Rogosinski, Fourier Series. 2nd ed. Cambridge Univ. Press, 1950. H. Hasse, Zahlentheorie. Akad.-Verlag, 1949. S. Helgason, Differential Geometry and Symmetric Spaces. Academic Press, 1962. K. Hensel, Theorie der Algebraischen Zahlen. Teubner, 1908. and G. Landsberg, Theorie der Algebraischen Functionen einer Variabeln.... Leipzig, 1902. D. Husemoller, Fibre Bundles. McGraw-Hill, 1966. E. R. Kolchin, Differential Algebra and Algebraic Groups. Academic Press, 1973. E. Landau, "Theorie der Dirichletschen Reihen," Handbuch der Lehre von der Verteilung der Primzahlen, vol. 2, book 6, 2nd ed. Teubner, 1909. Serge Lang, Diophantine Geometry. Interscience, 1962. , Algebraic Numbers. Addison-Wesley, 1964. , Introduction to Diophantine Approximations. AddisonWesley, 1966. Introduction to Transcendental Numbers. Addisonm;, 1966. S. Lie and F. Engel, Theorie der Transformationsgruppen. Teubner, 1883-93; Chelsea, 1970. J. Lipman, Transcendental Numbers. Queen's Univ. Press, 1966. C. C. Mac Duffee, An Introduction to Abstract Algebra. Wiley, 1940. S. Mac Lane, Homology. Springer, 1963. John Milnor, Introduction to Algebraic K-Theory. Princeton Univ. Press, 1971. L. J. Mordell, "On the rational solutions of...[cubic and quartic equations]," Proc. Camb. Phil. Sot. 21 (1922), 179-92. L. Novf, Origins of Modern Algebra, translated by J. Taner. Prague, Academic Press, 1973. E. Picard, Trait6 d'dnalyse, vol. 3. Gauthier-Villars, 1898. I. Schur, Werke. Ges. Math. J. P. Serre, Corps Locaux. Hermann, 1962. , Lie Algebras and Lie Groups. Benjamin, 1965. &pres&ntations
Lindaires
des Groups Finis.
EAn, 1967. C. L. Siegel, "Approximation algebraischen Zahlen," Math. Zeits. 10 (1921), 173-213. N. E. Steenrod, The Topology ofFibre Bundles. Princeton Univ. Press, 1951. E. Steinitz, "Algebraische Theorie der Ktirper," J. reine
Bibliographies
HM2
D52. D53. D54. D55. D56. D57. D58. D59. D60. D61,
ang. r@th. 137 (1910), 167-309. Republished with an appendix by R. Baer and H. Hasse, de Gruyter, 1939; Chelsea, 1951. algebraische Zahlen," J. A. Thue, "uber Anngherungswerte reine ang. Math. 135 (1909), 284-305. R. S. Varga, Matrix Iterative Analysis. Prentice-Hall, 1962. E. Vessiot, "Methodes d'int6gration elGmentaires," Encyclopedic des sci. math. pures et appliqu&es, tome II, vol. 3, fast. 1 (1910). sur les courbes alg8briques," A. Weil, "L'arithmEtique Acta Math. 52 (1929), 281-315. "Sur un ThBorBme de Mordell ,'I Bull. Sci. Math. 54 (193oj, 182-191. , Vari.56 lCdhl6riennes. Hermann, 1958. Springer, 1967. r Basic Number Theory. H. Whitney, Topological Groups. Lecture Notes, Harvard, 1936. J. H. Wilkinson, The Algebraic Eigenvalue Problem. Clarendon Press, 1956. 0. Zariski, Collected Papers (H. Hironaka and D. Mumford, eds.). MIT Press, 1972-. E-
El. E2. E3. E4. ES. E6. E7.
E8. E9.
613
ANALYSIS
S. Banach, Th&oorie des Opkations 2nd ed., Chelsea, 1962. E. F. Beckenbach and R. Bellman, 1971. A Collection
L&&ares.
Warsaw, 1933;
Inequalities.
Springer,
of Modern Mathematical
Classics:
Analysis,
ed. R. Bellman. Dover, 1961. M. Bernkopf, "The development of function spaces...," See also Archive Hist. Exact Sci. 3 (1966-67), l-96. ibid. 4 (1968), 308-58. G. Birkhoff, edited with the assistance of U. Merzbach, A Source Book in Classical Analysis. Harvard Univ. Press, 1973. 0. Bolza, Lectures on the Calculus ofvariations. Chicago Univ. Press, 1904. Stephen G. Brush, "Functional integrals and statistical physics," Rev. Mod. Phys. 33 (1961), 79-92; "A history of random processes, I . . ..." Archive Hist. Exact Sci. 5 "Mach and atomism," Synthese 18 (1968), (1968), l-36; 192-215. J. B. Diaz and John M. Bownds, "Euler-Cauchy polygons and the local existence of solutions to abstract ordinary differential equations," Funkc. Ekv. 15 (1972), 193-207. and F. T. Metcalf, "Complementary inequalities. I,"
614
G. Birkhoff J. Math.
ElO. Ell. E12. E13. E14. E15. E16.
E18. E19. E20. E21. E22.
Appl.
E24. E25. E26. E27. E28. E29. E30. E31.
39-74.
l-36.
0. D. Kellogg, Foundations of Potential Theory. Springer, 1929. theory and its significance...," George W. Mackey, "Ergodic Advances in Math. 12 (1974), 178-268. J. H. Manheim, The Genesis of Point Set Topology. Macmillan, 1964. A. F. Monna, Functional Analysis in Historical Perspective. 1973; see also "The concept Osthoek Publ. Co., Utrecht, of function..., I' Archive Hist. Exact Sci. 9 (1972), 57-84. E. H. Moore, Introduction to a Form of General Analysis. The New Haven Colloquium. Yale Univ. Press, 1910. C. B. Morrey, Multiple Integrals in the Calculus of Variations. Springer, 1966. See also Lecture Notes on the Theory of Elliptical
E23.
9 (1964),
HM2
Garwood
and F. T. Metcalf, "An analytic proof of Young's inequality," Am. Math. Monthly 77 (1970), 603-9. "Sur quelques points du calcul fonctionnel," M. Fr&het, Rendic. Sot. Mat. Palermo 22 (1906), l-74. P. Halmos, "Mathematics as a creative art," American Scientist (1968), 375-389. G. H. Hardy, D. E. Littlewood and G. P6lya, Inequalities. Cambridge Univ. Press, 1934. T. W. Hawkins, Lebesgue's Theory of Integration, its Origins Univ. Wisconsin Press, 1970. and Developments. D. Hilbert, Griindzuge einer allgemeinen theorie der Teubner, 1912; Chelsea linearen Integralgleichungen. reprint, 1953. "Motion of the lunar perigee...," Acta Math. G. W. Hill, 8 (1886),
E17.
Anal.
& S.A.
Partial
Differential
Equations.
Univ. of Chicago, 1960. de l'integrabilite des &quations G. Peano, "DEmonstration differentielles ordinaires," Math. Annalen 37 (1890), (A pioneer paper written in Peano's symbolic 182-228. logic.) 0. Perron, "Ein neuer Existenzbeweis fiir die Integrale der D'gleichung y' = f(x,y)," Math. Annafen 76 (1915), 471-84. H. Poincare, Les M&thodes Nouvelles de la Mdchanique Cgleste, 3 Vols. Gauthier-Villars, 1892-1899. Bernhard Riemann, Gesammelte Mathematische Werke, 2nd ed. Teubner, 1892; Dover, 1953. F. Riesz, "Untersuchungen Uber Systeme integrierbarer Funktionen," Math. Annalen 69 (1910), 449-495. , Les d'lnconnues.
SystZ‘mes
d'Equations
Lingaires
2 une Infinit6
Gauthier-Villars, 1913. "fiber Lineare Funktionalgleichungen," Acta Math. 41119181. 71-98. S. Saks ,'Th&orie de 1'Intkgrale. Warsaw, 1933. J. A. Shohat and J. D. Tamarkin, The Problem of Moments. Am. Math. Sot., 1943.
HM2 E32.
Bibliographies
615
E. M. Stein,
Singular Integrals and Differentiability of Functions. Princeton Univ. Press, 1970. and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces. Princeton Univ. Press, 1971. M. H. Stone, Linear Transformations in Hilbert Space. Properties
E33. E34. E3.5. E36. E37. E38.
Am. Math. Sot., 1932. E. C. Tit&marsh, Eigenfunction Expansions. Clarendon Press, 1946. The Analytical Foundations of Celestial A. Wintner, Mechanics. Princeton Univ. Press, 1941. Z. Zygmund, Trigonometric Series, 2 ~01s. Cambridge Univ. Press, 1968. , "IntQgrales Singulikres." Springer Lecture Notes in Math. #204 (1971).